Angle
Given two intersecting Lines or Line Segments, the amount of Rotation aboutthe point of intersection (the Vertex) required to bring one into correspondence with the other is called the angle
between them. Angles are usually measured in Degrees (denoted °),Radians (denoted rad, or without a unit), or sometimes Gradians (denoted grad).
One full rotation in these three measures corresponds to 360°, 
rad, or 400 grad. Half a fullRotation is called a Straight Angle, and a Quarter of a full rotation is called a Right Angle. An angle less than a Right Angle is called an Acute Angle, and an angle greater than a Right Angle iscalled an Obtuse Angle.
The use of Degrees to measure angles harks back to the Babylonians, whose Sexagesimal numbersystem was based on the number 60. 360° likely arises from the Babylonian year, 
which was composed of360 days (12 months of 30 days each). The Degree is further divided into60 Arc Minutes, and an Arc Minute into 60 Arc Seconds. A more naturalmeasure of an angle is the Radian. It has the property that the Arc Length around a Circle is simplygiven by the radian angle measure times the Circle Radius. The Radian is also the most useful anglemeasure in Calculus because the Derivative of Trigonometric functions such as
does not require the insertion of multiplicative constants like
. Gradians are sometimes usedin surveying (they have the nice property that a Right Angle is exactly 100 Gradians), but areencountered infrequently, if at all, in mathematics.The concept of an angle can be generalized from the Circle to the Sphere. The fraction of a Spheresubtended by an object is measured in Steradians, with the entire Sphere correspondingto 
Steradians.
A ruled Semicircle used for measuring and drawing angles is called a Protractor. A Compasscan also be used to draw circular Arcs of some angular extent.
See also Acute Angle, Arc Minute, Arc Second, Central Angle, Complementary Angle,Degree, Dihedral Angle, Directed Angle, Euler Angles, Gradian, Horn Angle,Inscribed Angle, Oblique Angle, Obtuse Angle, Perigon, Protractor, Radian,Right Angle, Solid Angle, Steradian, Straight Angle, Subtend, Supplementary Angle,Vertex Angle
References
Dixon, R. Mathographics. New York: Dover, pp. 99-100, 1991.
- Robertson-Seymour Theorem
- Robin Boundary Conditions
- Robin's Constant
- Robinson Projection
- Robust Estimation
- Rodrigues Formula
- Rodrigues's Curvature Formula
- Rogers-Ramanujan Continued Fraction
- Rogers-Ramanujan Identities
- Rolle's Theorem
- Roman Coefficient
- Roman Factorial
- Roman Numeral
- Roman Surface
- Roman Symbol
- Romberg Integration
- Rook Number
- Rook Reciprocity Theorem
- Rooks Problem
- Room Square
- Root
- Root Dragging Theorem
- Rooted Tree
- Root Linear Coefficient Theorem
- Root-Mean-Square